24 citations · 134 across the 22 of their papers we have counts for
23 papers
On the geometry of geometric rank
Runshi Geng, J. M. Landsberg
We make a geometric study of the Geometric Rank of tensors recently introduced by Kopparty et al. Results include classification of tensors with degenerate geometric rank in $C^3\o…
A lower bound for the border rank of matrix multiplication
J. M. Landsberg, Mateusz Michałek
Let M_n denote the matrix multiplication tensor for nxn matrices. We use the border substitution method combined with Koszul flattenings to prove the border rank lower bound of 2n^…
On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry
J. M. Landsberg, Mateusz Michałek
We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors w…
An introduction to geometric complexity theory
J. M. Landsberg
I survey methods from differential geometry, algebraic geometry and representation theory relevant for the permanent v. determinant problem from computer science, an algebraic anal…
On minimal free resolutions of sub-permanents and other ideals arising in complexity theory
Klim Efremenko, J. M. Landsberg, Hal Schenck +1
We compute the linear strand of the minimal free resolution of the ideal generated by k x k sub-permanents of an n x n generic matrix and of the ideal generated by square-free mono…
Abelian Tensors
J. M. Landsberg, Mateusz Michałek
We analyze tensors in the tensor product of three m-dimensional vector spaces satisfying Strassen's equations for border rank m. Results include: two purely geometric characterizat…